Engineering - Heat Transfer Formulas.pdf

HEAT TRANSFER FORMULAE Conduction Resistances in series: Q =

Q =

Ti − To xm 1 + + hc A kA

Plane Walls

1 hco A

2π ( ∆Tio ) r 1 1 + n n +1 + hci ri kn rn

Cylinders

1 hc0 r0

Temperature along a fin:

θ = c1e mx + c2e − mx

where m 2 =

hc S kA

Heat flux at the base of a fin: Q 0 = θ 0 (hc SkA)

1 2

1 ö æ hc S 2 ÷ ç tanhç ç ÷ ÷ kA è

Convection

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Transport Groups Reynolds' No. Grashof No. Nusselt No. Friction Factor

•

•

ρud µ βgL3 ( ∆T ) Gr = υ2 h d Nu = c k 2d 1 f = ∆p. . 2 L ρu Re =

State Groups

Cp µ

Prandtl No.

Pr =

Mach No.

u M= a

Combined Groups

k

Nu Re. Pr

Stanton No.

St =

Peclet No.

Pe = Re. Pr

Rayleigh No.

Ra = Gr. Pr

1

HEAT TRANSFER FORMULAE

Convection along Plates and Tubes FORCED Plate Nu =

Laminar

1 0 ⋅ 664 Re 2

Nu = 0 ⋅ 036 Re

Turbulent

Tube Nu = 4 ⋅ 364 Q = const . Nu = 3 ⋅ 658 Tw = const .

1 Pr 3

0⋅8

1 Pr 3

Nu = 0 ⋅ 023 Re =

1 3 Re Pr

f

1 3 Pr

0⋅ 8

8

FREE Laminar

Vertical Tube:

Vertical Plate: 1 4

4 Gr Nu = ç L ÷ g. Pr 3 4

Nu =

1 0 ⋅ 902 Pr 2

( 0 ⋅ 861 + Pr ) Horizontal:

1 4

Horizontal:

Nutop = 0 ⋅ 14( Gr. Pr ) Nubot . = 0 ⋅ 27( Gr. Pr ) Turbulent

1

Gr 4 ç ÷ 4

1 3

Nu = 0 ⋅ 53( Gr Pr )

1 4

1 4

Vertical: Nu = 0 ⋅ 54( Gr Pr )

1 4

HEAT EXCHANGERS

∆Tm = LMTD =

∆T1 − ∆T2 lnç

∆T1 ÷ ∆T2

∈=

C (Ti − To ) Cmin T − T ′ i i

∈=

UA / Cmin ) − 1+ C / C 1 − e ( min max ) ( 1 + Cmin / Cmax

(

)

Radiation

A1 12 =

Q comb =

1 ö 1 æ 1 ö 1 æ 1 1 ç − 1÷ + ç − 1÷ + A1 è ∈1 A2 è ∈2 A1F12 T1 − T2

æç x ö÷ + è Ak

1 A(hc + ha )

2